Low temperature nonequilibrium dynamics in transverse Ising spin glass

The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature T ₁ (lower than the spin glass transition temperature T _g ) the ac susceptibility decreases with time approximately in a logarithmic way as the system tends to the equilibrium. It is shown that the transverse field of tunneling has unessential effect on the nonequilibrium dynamical properties of the magnetic droplet system. The role of quantum fluctuations in the behavior of the ac susceptibility is discussed.Received: 26 February 2004, Published online: 18 June 2004PACS: 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.10.Nr Spin-glass and other random models - 75.50.Lk Spin glasses and other random magnets     

Strong universality and algebraic scaling in two-dimensional Ising spin glasses

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but nonzero temperatures and provide numerical evidence that eta approximately equal 0 and nu approximately equal 3.5 in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds, in particular, for the +/- J model, with or without dilutions, and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T = 0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.     

Test of universality in anisotropic 3D Ising model

Chen and Dohm predicted theoretically in 2004 that the widely believed universality principle is violated in the Ising model on the simple cubic lattice with more than only six nearest neighbours. Schulte and Drope by Monte Carlo simulations found such violation, but not in the predicted direction. Selke and Shchur tested the square lattice. Here, we check only this universality for the susceptibility ratio near the critical point. For this purpose we study first the standard Ising model on a simple cubic lattice with six nearest neighbours, then with six nearest and 12 next-nearest neighbours, and compare the results with the Chen–Dohm lattice of six nearest neighbours and only half of the 12 next-nearest neighbours. We do not confirm the violation of universality found by Schulte and Drope in the susceptibility ratio.     

Nonequilibrium dynamics in two-dimensional Ising spin glass

This paper investigates the nonequilibrium dynamics of two-dimensional Ising spin glass by dynamical Monte Carlo simulations. A new method is developed to quantitatively measure the age of domain growth. Using this method it investigates how temperature shift affects the effective age of domain growth. It finds that the T -shift dependence of the effective age follows the prediction of the droplet model quite well. It also investigates the overlap length between the spin glass states as well as the correlated flips of spins,which are not consistent with the theoretical predictions. The possible reasons are discussed.     

Finite interaction range spin glass in the Ising model

Using the Ising model and the random-field approximation, it is demonstrated that, in amorphous diluted magnets and crystalline metal alloys, the nearest neighbor interaction promotes a superparamagnetic state, which is followed by “freezing” of the magnetic moments of clusters and by transition into a macrospin glass state (cluster spin glass) as the temperature decreases. A theoretical magnetic phase diagram is constructed.     

Partition function zeros and the three-dimensional Ising spin glass

We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×L_z, 4×4×L_z, and 5×5×L_z forL _z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.     

Critical thermodynamics of the two-dimensional +/-J Ising spin glass

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low lying excitations and by the way low energy domain walls proliferate in this model.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

Microscopic description of an Ising spin glass near the percolation threshold

Monte Carlo results using a microscopic model to describe FexZn(1-x)F2 indicate that its spin-glass phase at x=0.25 and zero magnetic field is characterized by the presence of antiferromagnetic fractal domains, separated by random vacancies and strongly correlated in time. The effective local random-field distribution corroborates this glassy behavior, which emerges irrespective of ab initio competing interactions and is a consequence of the fractal domain structure near the percolation threshold, x(p)=0.24. The aging properties of the system are in agreement with predictions of short-range stochastic spin-glass models and with the droplets model for spin glass close to percolation.